No. of visible lines when an electron returns from `5^(th)` orbit up to ground state in `H`spectrum :

Options

A. 5
B. 4
C. 3
D. 10

Explanation

To find the number of visible lines when an electron returns from the 5th orbit to the ground state in the hydrogen spectrum, we can use the concept of electronic transitions and the Rydberg formula.

### Step-by-Step Solution:

1. **Understanding the Energy Levels**:
In a hydrogen atom, the energy levels are quantized and given by the formula:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
where \( n \) is the principal quantum number.

2. **Identifying the Transition**:
The electron transitions from the 5th orbit (n=5) to the ground state (n=1). The possible transitions from n=5 to n=1 can be calculated by considering all intermediate levels (n=2, n=3, n=4).

3. **Calculating Possible Transitions**:
The possible transitions from n=5 to lower energy levels are:
- 5 to 4
- 5 to 3
- 5 to 2
- 5 to 1
- 4 to 3
- 4 to 2
- 4 to 1
- 3 to 2
- 3 to 1
- 2 to 1

We can summarize the transitions as follows:
- From n=5 to n=4, n=3, n=2, and n=1 (4 transitions).
- From n=4 to n=3, n=2, and n=1 (3 transitions).
- From n=3 to n=2 and n=1 (2 transitions).
- From n=2 to n=1 (1 transition).

The total number of transitions is:
\[ 4 + 3 + 2 + 1 = 10 \]

4. **Identifying Visible Lines**:
In the hydrogen spectrum, the visible lines correspond to transitions that fall within the Balmer series, which includes transitions to the n=2 level. The visible transitions from n=5 are:
- 5 to 2
- 4 to 2
- 3 to 2
- 2 to 2 (not counted as it’s not a transition)

Thus, the visible transitions are:
- 5 to 2
- 4 to 2
- 3 to 2

Therefore, there are **3 visible lines** when the electron returns from the 5th orbit to the ground state.

### Final Answer:
The number of visible lines when an electron returns from the 5th orbit to the ground state in the hydrogen spectrum is **3**.